We review and develop two little known results on the equality of mixed
partial derivatives which can be considered the best results so far available
in their respective domains. The former, due to Mikusi\'nski and his school,
deals with equality at a given point, while the latter, due to Tolstov,
concerns equality almost everywhere. Applications to differential geometry and
General Relativity are commented.Comment: 17 pages. v2: Added reference to Mikusinski's works. v3: Corrected a
product set statement in Theorem
